Given two integers A and B, representing the length of semi-major and semi-minor axis of an Ellipse with general equation (x2 / A2) + (y2 / B2) = 1, the task is to find the length of the latus rectum of the ellipse
Examples:
Input: A = 3, B = 2
Output: 2.66666Input: A = 6, B = 3
Output: 3
Approach: The given problem can be solved based on the following observations:
- The Latus Rectum of an Ellipse is the focal chord perpendicular to the major axis whose length is equal to:
Ellipse
- Length of major axis is 2A.
- Length of minor axis is 2B.
- Therefore, the length of the latus rectum is:
Follow the steps below to solve the given problem:
- Initialize two variables, say major and minor, to store the length of the major-axis (= 2A) and the length of the minor-axis (= 2B) of the Ellipse respectively.
- Calculate the square of minor and divide it with major. Store the result in a double variable, say latus_rectum.
- Print the value of latus_rectum as the final result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <iostream>using namespace std;// Function to calculate the length// of the latus rectum of an ellipsedouble lengthOfLatusRectum(double A, double B){ // Length of major axis double major = 2.0 * A; // Length of minor axis double minor = 2.0 * B; // Length of the latus rectum double latus_rectum = (minor*minor)/major; return latus_rectum;}// Driver Codeint main(){ // Given lengths of semi-major // and semi-minor axis double A = 3.0, B = 2.0; // Function call to calculate length // of the latus rectum of a ellipse cout << lengthOfLatusRectum(A, B); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{// Function to calculate the length// of the latus rectum of an ellipsestatic double lengthOfLatusRectum(double A, double B){ // Length of major axis double major = 2.0 * A; // Length of minor axis double minor = 2.0 * B; // Length of the latus rectum double latus_rectum = (minor * minor) / major; return latus_rectum;}// Driver codepublic static void main(String[] args){ // Given lengths of semi-major // and semi-minor axis double A = 3.0, B = 2.0; // Function call to calculate length // of the latus rectum of a ellipse System.out.print(lengthOfLatusRectum(A, B));}}// This code is contributed by susmitakundugoaldanga |
Python3
# Python3 program for the above approach# Function to calculate the length# of the latus rectum of an ellipsedef lengthOfLatusRectum(A, B): # Length of major axis major = 2.0 * A # Length of minor axis minor = 2.0 * B # Length of the latus rectum latus_rectum = (minor*minor)/major return latus_rectum# Driver Codeif __name__ == "__main__": # Given lengths of semi-major # and semi-minor axis A = 3.0 B = 2.0 # Function call to calculate length # of the latus rectum of a ellipse print('%.5f' % lengthOfLatusRectum(A, B)) # This code is contributed by ukasp. |
C#
// C# program for the above approachusing System;class GFG{ // Function to calculate the length // of the latus rectum of an ellipse static double lengthOfLatusRectum(double A, double B) { // Length of major axis double major = 2.0 * A; // Length of minor axis double minor = 2.0 * B; // Length of the latus rectum double latus_rectum = (minor*minor)/major; return latus_rectum; } // Driver Code public static void Main() { // Given lengths of semi-major // and semi-minor axis double A = 3.0, B = 2.0; // Function call to calculate length // of the latus rectum of a ellipse Console.WriteLine(lengthOfLatusRectum(A, B)); }}// This code is contributed by souravghosh0416. |
Javascript
<script>// Javascript program for the above approach// Function to calculate the length// of the latus rectum of an ellipsefunction lengthOfLatusRectum(A, B){ // Length of major axis var major = 2.0 * A; // Length of minor axis var minor = 2.0 * B; // Length of the latus rectum var latus_rectum = (minor * minor) / major; return latus_rectum;}// Driver code// Given lengths of semi-major// and semi-minor axisvar A = 3.0, B = 2.0;document.write(lengthOfLatusRectum(A, B));// This code is contributed by Ankita saini </script> |
Output
2.66667
Time Complexity: O(1)
Auxiliary Space: O(1)
Using the formula :
Approach:
The length of the Latus Rectum of an Ellipse can be calculated using the formula: L = 2b^2/a, where a and b are the lengths of the major and minor axis of the ellipse, respectively.
Define a function latus_rectum that takes two arguments a and b.
Inside the function, calculate the length of the Latus Rectum using the formula 2 * b ** 2 / a and return the result.
Call the function twice with different values of a and b.
Print the results using formatted strings to display the inputs and outputs with appropriate decimal places.
C++
#include <iostream>#include <iomanip> // For setting the precision of the output// Function to calculate the length of Latus Rectumdouble latusRectum(double a, double b) { return (2 * b * b) / a;}int main() { // Example inputs double a1 = 3, b1 = 2; double a2 = 6, b2 = 3; // Calculate the length of Latus Rectum for the first ellipse double l1 = latusRectum(a1, b1); // Display the result with formatted string std::cout << "The length of the Latus Rectum of the ellipse with a = " << a1 << " and b = " << b1 << " is " << std::fixed << std::setprecision(5) << l1 << std::endl; // Calculate the length of Latus Rectum for the second ellipse double l2 = latusRectum(a2, b2); // Display the result with formatted string std::cout << "The length of the Latus Rectum of the ellipse with a = " << a2 << " and b = " << b2 << " is " << std::fixed << std::setprecision(5) << l2 << std::endl; return 0;} |
Java
public class Main { // Function to calculate the length of Latus Rectum static double latusRectum(double a, double b) { return (2 * b * b) / a; } public static void main(String[] args) { // Example inputs double a1 = 3, b1 = 2; double a2 = 6, b2 = 3; // Calculate the length of Latus Rectum for the first ellipse double l1 = latusRectum(a1, b1); // Display the result with formatted string System.out.println("The length of the Latus Rectum of the ellipse with a = " + a1 + " and b = " + b1 + " is " + String.format("%.5f", l1)); // Calculate the length of Latus Rectum for the second ellipse double l2 = latusRectum(a2, b2); // Display the result with formatted string System.out.println("The length of the Latus Rectum of the ellipse with a = " + a2 + " and b = " + b2 + " is " + String.format("%.5f", l2)); }}// This code is contributed by shivamgupta0987654321 |
Python3
def latus_rectum(a, b): return 2 * b ** 2 / a# Example inputsa1, b1 = 3, 2a2, b2 = 6, 3# Calculate the length of Latus Rectum for the first ellipsel1 = latus_rectum(a1, b1)# Display the result with formatted stringprint(f"The length of the Latus Rectum of the ellipse with a = {a1} and b = {b1} is {l1:.5f}")# Calculate the length of Latus Rectum for the second ellipsel2 = latus_rectum(a2, b2)# Display the result with formatted stringprint(f"The length of the Latus Rectum of the ellipse with a = {a2} and b = {b2} is {l2:.5f}") |
Output
The length of the Latus Rectum of the ellipse with a = 3 and b = 2 is 2.66667 The length of the Latus Rectum of the ellipse with a = 6 and b = 3 is 3.00000
Time complexity: O(1)
Auxiliary Space: O(1)
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!